8-62 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} k&=200\ut{N/m}\\ mg&=20\ut{N}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \LE : \text{Elastic Potential Energy}\\ \end{cases} $$ $$ \begin{aligned} \Delta \GE(y_f)&=\Delta(mgy)\\ &=mg \Delta y\\ &=mg (y_f-y_i)\\ &=mg y_f\\ &=20 y_f\taag 1\\ \end{aligned} $$ $$\Delta x=-\Delta y$$ $$x_f=-y_f$$ $$ \begin{aligned} \Delta \LE(y_f)&=\Delta\(\frac{1}{2}kx^2\)\\ &=\frac{1}{2}k\Delta\(x^2\)\\ &=\frac{1}{2}k\({x_f}^2-{x_i}^2\)\\ &=\frac{1}{2}k{y_f}^2\\ &=100{y_f}^2\taag2\\ \end{aligned} $$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE+\Delta \LE=0$$ $$ \begin{aligned} \Delta \KE(y_f)&=-\Delta \GE-\Delta \LE\\ &=-20y_f-100{y_f}^2\taag3\\ \end{aligned} $$ $$ \therefore \begin{cases} \Delta \KE(-y)&=20y-100y^2\\ \Delta \GE(-y)&=-20 y\\ \Delta \LE(-y)&=100y^2\\ \end{cases} $$ $$\ab{a,b,c}$$ $$y=-5.0\ut{cm}=-0.05\ut{m}$$ $$ \begin{cases} \Delta \KE &=\frac{3}{4}\ut{J}=0.75\ut{J}\\ \Delta \GE &=-1\ut{J}\\ \Delta \LE &=\frac{1}{4}\ut{J}=0.25\ut{J}\\ \end{cases} $$ $$\ab{d,e,f}$$ $$y=-10\ut{cm}=-0.1\ut{m}$$ $$ \begin{cases} \Delta \KE&=1\ut{J}\\ \Delta \GE&=-2\ut{J}\\ \Delta \LE&=1\ut{J}\\ \end{cases} $$ $$\ab{g,h,i}$$ $$y=-15.0\ut{cm}=-0.15\ut{m}$$ $$ \begin{cases} \Delta \KE&=\frac{3}{4}\ut{J}=0.75\ut{J}\\ \Delta \GE&=-3\ut{J}\\ \Delta \LE&=\frac{9}{4}\ut{J}=2.25\ut{J}\\ \end{cases} $$ $$\ab{j,k,l}$$ $$y=-20\ut{cm}=-0.20\ut{m}$$ $$ \begin{cases} \Delta \KE&=0\\ \Delta \GE&=-4\ut{J}\\ \Delta \LE&=4\ut{J}\\ \end{cases} $$